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42615-G10
Fluctuating Magnetic Moments in Non-Magnetic Liquids
A discrepancy in scattering power has been observed in experiments on liquid metals using neutron scattering on the one hand, and X-ray scattering on the other hand. More neutrons were being deflected than anticipated. We postulated that this might be because some ions in the liquid might be magnetic, thereby deflecting the neutron which itself is a small magnet. We have been investigating whether some liquid metals do indeed harbor a small fraction of magnetic ions, even though the liquid as a whole is non-magnetic. 
Our proposed mechanism by which magnetic moments can exist in a non-magnetic liquid is straightforward [see figure]. Magnetic moments fluctuating on a very short timescale could be the direct result of collision induced valence changes [when ions collide, an electron from a filled shell is ejected into the sea of conduction electrons (b), leaving behind a local moment (c). The electron is recaptured a short time later (d)]. This process would give rise to a magnetic cross-section in neutron scattering experiments, with the moments popping in and out of existence on the same time scale as the cage diffusion process [where an ion rattles around in the cage formed by its neighbors, repeatedly colliding with them].
Through a literature study [Physical Review E 73, 021202 (2006)] we found strong [indirect] evidence for the existence of such moments in the heavier metallic elements Hg and Pb. In liquid mercury we found an excess in the reported number of neutrons deflected over small angles, and from published quasi-elastic neutron scattering data we were able to confirm that this cross-section was associated with ionic motion on the time scale of cage-diffusion. The data indicated that as many as 20% of the Hg ions are missing electrons at any given time.
Also, literature data on liquid Ga seemed to indicate that this system might also harbor magnetic moments as it displayed an excess cross-section with a cage diffusion signature. However, through a polarized neutron scattering study, we showed that this system does not have a magnetic response. We followed up with an extensive series of unpolarized neutron scattering experiments employing various experimental configurations, and we have now concluded that in liquid Ga the excess scattering reported by various groups is the result of multiple scattering. These results have been submitted for publication.
Despite the absence of magnetic moments in liquid Gallium, we believe that Hg is still very likely to harbor magnetic moments. The reason is that the very same data analysis procedure that we used to identify the excess scattering in Ga as multiple scattering failed to link the excess scattering seen in Hg to multiple scattering. Unfortunately, it is not possible to do experiments on Hg at a reactor based neutron source, but experiments on liquid Pb [requiring a furnace] should provide the final verdict on whether such short-lived moments exist or not.
As a follow up to the research into the behavior of liquid Hg and Ga, we are investigating whether observed differences between the two with respect to their very short time behavior reflect an intrinsic difference, or whether it can be understood on general quantum mechanical grounds. Even though Ga and Hg are similar in many ways, there is a subtle difference when it comes to binary collisions. For liquid Hg these collisions are very well described as being collisions between hard-sphere particles of standard diameter. However, while the hard-sphere description for the liquid phase of Ga also yielded excellent numerical agreement, the inferred hard-sphere diameters were by too large by far. This either implies that larger structural units are present in Ga (a very interesting possibility and the current frontrunner as proposed by Scopigno and co-workers), or it may be that remnant quantum mechanical diffraction effects (such as those present in liquid helium under similar conditions) skew the Ga numbers.
In order to ascertain whether diffraction plays a role, we are numerically solving the quantum mechanical collision problem between two Ga atoms. Since Ga is an almost classical liquid [as opposed to liquid He], we are including quantum numbers up to very high values, rendering this computation somewhat computer intensive. However, given the fact that such diffraction effects have been observed in molecular beam collisions between sodium ions [i.e., much heavier ions that He atoms], this calculation seems a worthwhile endeavor. Either outcome will be welcome: the absence of diffraction effects would put the presence of larger structural units in Ga on a more solid footing, whereas their presence would remove the need to use unphysically large hard-sphere diameters in order to properly describe Ga.
The research described above constitutes the thesis work of Mark Patty and is projected to be finished by 1/08.
